Find the volume of the solid obtained by rotating the region underneath the graph of the function over the given interval about the 𝑦- axis.

Question

f(x) = √x^2 + 4 , [0,1]

the square root is over the entire equation not just the x^2

Answer 1

By Shell Method volume v = 2π∫₀¹x√(x² + 4)dx =2/3π(x² + 4)^3/2₀¹ = 2/3π(5^3/2 - 8) = 6.661

Answer 2

Cylindrical shell seems the best approach:

integral from x = 0 to 1 of (2πxf(x))dx or 2π integral from x = 0 to 1 of sqrt(x²+4)xdx

That is integrable: (1/2)2π(2/3)(x²+4)^3/2 from 0 to 1

(2π/3)(5^3/2-8)

Please consider a tutor. Take care